Farrukh Mukhamedov, Utkir Rozikov, Jose Fernando F. Mendes
Published 2005-12-07, updated 2006-02-25Version 2
In the paper we considere three state $p$-adic Potts model with competing interactions on a Cayley tree of order two. We reduce a problem of describing of the $p$-adic Gibbs measures to the solution of certain recursive equation, and using it we will prove that a phase transition occurs if and only if $p=3$ for any value (non zero) of interactions. As well, we completely solve the uniqueness problem for the considered model in a $p$-adic context. Namely, if $p\neq 3$ then there is only a unique Gibbs measure the model.
Comments: 12 pages, to appear in the Proceedings of the '2nd International Conference on p-Adic Mathematical Physics' (Belgrade, 15-21 September 2005) published by AIP Conference Proceedings
Journal: Proceedings of the '2nd International Conference on p-Adic Mathematical Physics' (Belgrade, 15-21 September 2005) published by AIP Conference Proceedings, Vol. 826, 2006, pp.140-150
On Inhomogeneous $p$-Adic Potts Model on a Cayley Tree
On Gibbs Measures of $P$-Adic Potts Model on the Cayley Tree
On Uniqueness of Gibbs Measures for $P$-Adic Nonhomogeneous $ł$-Model on the Cayley Tree
